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This paper develops Bayesian weighted instrumental variable (WIV) estimators under equality and inequality speed constraints for the three-dimensional (3-D) bearings-only target motion analysis (TMA) problem, which show improved estimation accuracies compared to their unconstrained counterpart. Incorporating the speed constraint information into our previously proposed Bayesian WIV estimator imposes a quadratic constraint on this problem. Finding an optimal solution for the resulting nonconvex problem is by no means straightforward. The main problem with iterative optimization methods such as the maximum aposteriori is that they require initialization and may converge to a local minimum if poorly initialized.Using advanced linear and nonlinear algebra techniques, non-iterative accurate estimators under equality and inequality constraints are developed for this problem.Furthermore, it is proven that the proposed equality constrained estimator is approximately asymptotically unbiased and that the inequality constrained estimator is the optimal solution. An approximate covariance matrix has also been developed for the constrained WIV under equality constraint. Simulation results indicate that the equality and inequality constrained estimators outperform their unconstrained counterpart in the simulated scenarios. Refereed/Peer-reviewed

Refereed/Peer-reviewed Pharmacokinetic (PK) models are widely used to describe drug permeation across the epidermal membrane barrier, the stratum corneum (SC). Here, we extend our previously reported diffusion and compartment-in-series models to describe plasma concentrations, urinary excretion-time profiles and exposure estimates after topically applied finite doses of solvent deposited solids. In vivo models were derived by convolution of a skin absorption input function for finite dosing with that for in vivo disposition PK. In vitro skin permeation test (IVPT) and in vivo urinary excretion data for cortisone, desoxycorticosterone, and testosterone were extracted from literature for model validation and establishment of in vitro - in vivo relationships (IVIVR). Both SC diffusion and SC 3-compartment-in-series PK models adequately described experimental in vitro and in vivo permeation data, with similar model parameter estimates for SC diffusion time and bioavailability. A satisfactory IVIVR was generated for cortisone, whereas testosterone and desoxycorticosterone showed higher bioavailability in vitro compared to in vivo. In recognising that future prospective studies need to both have an adequate sampling schedule and be harmonized for robust IVIVRs, we developed expressions for predicting extent of absorption and time for peak absorption for both in vitro and in vivo studies. Other study parameters, such as application site, applied dose, and application techniques, can also affect drug permeability through skin during dosage form metamorphosis after finite dose application, and a lack of correlation may result if these are poorly matched.

Refereed/Peer-reviewed Topical products, widely used to manage skin conditions, have evolved from simple potions to sophisticated delivery systems. Their development has been facilitated by advances in percutaneous absorption and product design based on an increasingly mechanistic understanding of drug-product-skin interactions, associated experiments, and a quality-by-design framework. Topical drug delivery involves drug transport from a product on the skin to a local target site and then clearance by diffusion, metabolism, and the dermal circulation to the rest of the body and deeper tissues. Insights have been provided by Quantitative Structure Permeability Relationships (QSPR), molecular dynamics simulations, and dermal Physiologically Based PharmacoKinetics (PBPK). Currently, generic product equivalents of reference-listed products dominate the topical delivery market. There is an increasing regulatory interest in understanding topical product delivery behavior under ‘in use’ conditions and predicting in vivo response for population variations in skin barrier function and response using in silico and in vitro findings.

In this work, we developed a number of generalised skin diffusion based pharmacokinetic models to relate published in vivo urinary excretion data to matching experimentally generated in vitro human skin permeation test (IVPT) data for a series of topically applied salicylate esters. A simplified linear in vivo model was found to inadequately describe the time course of urinary excretion over the entire sampling period. We represented the skin barrier as both a one layer (stratum corneum) and a two-layer (stratum corneum with viable epidermis) diffusion model and convoluted their Laplace solutions with that for a single exponential disposition phase to describe the urinary excretion profiles in the Laplace domain. We also derived asymptotic approximations for the model and estimated the conditions under which they could be used. We then sought to develop in vitro - in vivo relationships (IVIVR) for topically applied methyl, ethyl and glycol salicylates using our experimental IVPT data and the literature urinary excretion data. Good linear IVIVRs for ethyl and glycol salicylates were obtained, but the IVIVR for methyl salicylate was poor, perhaps because of topical stimulation of local skin blood flow by methyl salicylate. The ratio of the hydrated to dehydrated skin permeation for all salicylate esters was the same in both the IVPT and in vivo studies. A diffusion based one compartment pharmacokinetic model was also developed to describe the urinary excretion of solutes after removal of topical products and to compare the methyl salicylate skin permeation for five different body sites. The work presented here is consistent with the development of skin IVIVRs, but suggests that different skin conditions, application sites and local skin effects may affect model predictions. Refereed/Peer-reviewed

The purpose of this volume is to present the theory of Markov and semi-Markov processes in a discrete-time, finite-state framework. Given this background, hidden versions of these processes are introduced and related estimation and filtering results developed. The approach is similar to the earlier book, Elliott et al. (1995). That is, a central tool is the Radon-Nikodym theorem and related changes of probability measure. In the discrete-time, finite-state framework that we employ these have simple interpretations following from Bayes' theorem.

We propose a model for the valuation of participating life insurance products under the Meixner process, which belongs to the family of semi-heavy tailed processes. This particular model assumption is extremely desirable as it captures the stylised features of the return distribution, with existing moment generating functions. The highlight of the paper is the analytical solution derived for minimising the relative entropy between the historical and risk-neutral measures, when driving a pricing kernel. Further, we capture the stochastic volatility effect using an accurate polynomial approximation technique. Finally, to highlight the practical applications, we conduct a simulation experiment. Refereed/Peer-reviewed

Most Australian capital cities require many 100,000s of additional dwellings to accommodate demographic change and population pressures in the next two or three decades. Urban growth will come in the form of infill, consolidation and urban expansion. Plans to redevelop environmental amenities such as parks and open green spaces are regularly being put forward to local councils and State governments. Maintaining parks and reserves represents one of the largest costs to local councils. To aid in the evaluation of some of the different propositions, we report the results of a spatial hedonic pricing model with fixed effects for Adelaide, South Australia. The results indicate that the private benefits of a close proximity to golf courses, green space sporting facilities, or the coast, are in the order $0.54, $1.58, and $4.99 per metre closer (when evaluated at the median respectively). The historic Adelaide Parklands add $1.55 to a property’s value for each additional metre closer. We demonstrate how the estimated model could be used to calculate how local private benefits capitalized in property values change with changes in the configuration of a park.

A cost process is associated with a discrete time, finite state Markov chain. Using backward recursion, the distribution of the first time the cost falls below a given level is calculated. Refereed/Peer-reviewed

This paper is a sequel to our previous paper ‘A New Paradigm in Asset Pricing’ in which we construct a model for asset pricing in a world where the randomness is modeled by a Markov chain. In this paper we develop a theory of optimal stopping and related variational inequalities for American options in this model. A version of Saigal's Lemma is established and numerical results obtained. Copyright © 2011 John Wiley & Sons, Ltd.

This paper demonstrates how to use distorted Gaussian copula functions to produce a heavy tailed portfolio loss distribution in the context of synthetic Collateralized Debt Obligations (CDOs). Distortion functions have not previously been used in this area. Hence, we demonstrate that it is possible to simulate realistic tranche prices by incorporating distorted copula functions within a well established CDO pricing system, such as that of JP Morgan. Furthermore, we only require a single dependence parameter for the entire portfolio rather than one per tranche. Thus, we are providing practitioners with a simpler and more flexible alternative to current CDO pricing methods.

Standard optimal portfolio choice models assume that investors maximise the expected utility of their future outcomes. However, behaviour which is inconsistent with the expected utility theory has often been observed.In a discrete time setting, we provide a formal treatment of risk measures based on distortion functions that are consistent with Yaari’s dual (non-expected utility) theory of choice (1987), and set out a general layout for portfolio optimisation in this non-expected utility framework using the risk neutral computational approach.As an application, we consider two particular risk measures. The first one is based on the PH-transform and treats the upside and downside of the risk differently. The second one, introduced by Wang (2000) uses a probability distortion operator based on the cumulative normal distribution function. Both risk measures rank-order prospects and apply a distortion function to the entire vector of probabilities.

The determination and allocation of economic capital is important for pricing, risk management, and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed-form results for the complete markets, arbitrage-free allocation of the insurer default option value, or insolvency exchange option, to lines of business for an insurer balance sheet. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multiline insurer. We discuss and illustrate other methods of capital allocation, including Myers-Read, and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line.

This paper discusses a class of risk measures developed from a risk measure recently proposed for insurance pricing. This paper reviews the distortion function approach developed in the actuarial literature for insurance risk. The proportional hazards transform is a particular case. The relationship between this approach to risk and other approaches including the dual theory of choice under risk is discussed. A new class of risk measures with suitable properties for asset allocation based on the distortion function approach to insurance risk is developed. This measure treats upside and downside risk differently. Properties of special cases of the risk measure and links to conventional portfolio selection risk measures are discussed. © 2000 Elsevier Science B.V. All rights reserved.

A continuous time financial market is considered where randomness is modelled by a finite state Markov chain. Using the chain, a stochastic discount factor is defined. The probability distributions of default times are shown to be given by solutions of a system of coupled partial differential equations. Refereed/Peer-reviewed

We propose new analytic approximations for the pricing of spread options. A spread option is an option whose payoff depends on the price spread between two underlying assets. Let S1(t) and S2(t) be the prices of the two assets. The payoff of a European spread call option with a strike price K and maturity T is (S1(T) − S2(T) − K)+. Valuation of such options, widely used in a number of financial markets, is fundamentally different from the valuation of other types of options. Since the behaviour of the spread is affected by the behaviour of two traded assets, it cannot be modelled as if it were simply a single asset. Moreover, the value of an option on a spread depends critically on the correlation between the price changes of the two underlying assets. Working under a risk-neutral probability measure, we assume that the underlying asset price processes are geometric Brownian motions with constant non-zero correlation. Using a perturbation expansion of the solution to the spread option price partial differential equation, we derive analytic formulae for approximations up to second order. We show that Kirk's (1995) approximation for spread options on energy futures, commonly used by traders, is an exact solution to a related problem, and corresponds to the n = 0 term in our perturbation expansion. Results from a numerical implementation of our approximations to spread option prices are then compared against those obtained by other approximation methods available in the literature.

This article fuses two pieces of theory to make a tractable model for asset pricing. The first is the theory of asset pricing using a stochastic discounting function (SDF). This will be reviewed. The second is to model uncertainty in an economy using a Markov chain. Using the semi-martingale dynamics for the chain these models can be calibrated and asset valuations derived. Interest rate models, stock price models, futures pricing, exchange rates can all be introduced endogenously in this framework. Refereed/Peer-reviewed

Titman (1985) famously applied optionality to derive the value of a vacant block of land then used as a car park at UCLA for which, in common with traditional property valuation approaches, a willing but not anxious buyer was assumed. However, what might the value of such a vacant block of land be in a property market downturn when willing but not anxious buyers are hesitant and there is an absence of comparable sales for reference? This paper applies concepts of optionality and indifference pricing to explore how such a vacant block of land might be considered relative to other, non-property asset classes to derive an assessment of value in the absence of an active property market. Refereed/Peer-reviewed

A discrete time nonlinear filter is used to estimate the volatility in a financial model. New filters are derived for sums of unobserved quantities and the EM algorithm applied to determine the parameters of the model. Refereed/Peer-reviewed

Recombining binomial tree models are very convenient for derivative pricing. But traditionally trinomial tree approximations are often used and have become a standard way of approximating continuous time interest rate models. We provide a methodology for using binomial models rather than trinomial models for such approximation and provide comparison with these trinomial approaches. We will demonstrate some advantages of these binomial models over the popular trinomial tree models We believe our approach is easier to apply and will perform better computationally and will help to improve some of the methods used by other researchers promoting lattice methods. The probabilities produced by our methodology are never negative for any discretization step length. The binomial model constructed by our method also preserves properties of the continuous time model like mean reversion

Summary Not only are copula functions joint distribution functions in their own right, they also provide a link between multivariate distributions and their lower-dimensional marginal distributions. Copulas have a structure that allows us to characterize all possible multivariate distributions, and therefore they have the potential to be a very useful statistical tool. Although copulas can be traced back to 1959, there is still much scope for new results, as most of the early work was theoretical rather than practical. We focus on simple practical tools based on conditional expectation, because such tools are not widely available. When dealing with data sets in which the dependence throughout the sample is variable, we suggest that copula-based regression curves may be more accurate predictors of specific outcomes than linear models. We derive simple conditional expectation formulae in terms of copulas and apply them to a combination of simulated and real data.

This article reviews the theory of fractional Brownian motion (fBm) in the white noise framework, and we present a new approach to the proof of Ito-type formulas for the stochastic calculus of fractional Brownian motion.

It is well established that volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence the volatility cannot be characterized by a single correlation time. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. In this paper we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat-tails. We aim to find the most probable path that contributes to the action functional, that describes the dynamics of the entire system, by finding local minima. We obtain a second order differential equation for the functional return. This paper reviews our current progress and the remaining open questions.